Assembly is the deliniated form of a processors native opcodes; some think of the instructions as 'macros' in a sense and others just think of them in terms of the correlation between the instruction and the emitted machine code the assembler produces (i.e. the correlation between the "add to accumulator" instruction and "0x12".) What it's based on is largely irrelivant in this situation, it has nothing to do with if or if not it is or is not something. C was based on B. Delphi was based on Pascal. Modern computers are still (largely) based on the von neumann architecture. Doesn't make much of an arguement to say that "[x] isn't [y] because it's based on [z]."
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I’m stating that there is a theory that concludes that for a supposed language to be classified as a language it has to be at the computational equivalent of a Turing machine.
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IOW, that language has to be
Turing Complete to be considered a language.